Practical feasibility of algorithmic approaches for discovering minimax decision rules at scale

Investigate the practical feasibility of implementing the ε-minimax optimization approach that discretizes the decision-rule space and uses first-order methods with a Nature best-response oracle (Aradillas Fernández, Blanchet, Montiel Olea, Qiu, Stoye, and Tan, 2025) and the fictitious-play approach for discretized finite statistical games (Guggenberger and Huang, 2025) to discover minimax-regret decision rules in statistical decision problems that are more complex than the stylized normal model with partial identification analyzed in Theorem 1.

Background

The paper emphasizes that closed-form derivations of minimax regret decision rules under partial identification are rare and often rely on problem-specific guess-and-verify tactics that do not scale well. To address this, the authors highlight two complementary algorithmic directions for discovering optimal or near-optimal rules: asymptotic simplifications and automated solution methods for statistical games.

They discuss two recent algorithmic approaches: an ε-minimax method that discretizes the decision-rule space and leverages multiplicative-weights-style, first-order optimization with an oracle for Nature’s best response, and a fictitious-play algorithm that approximately solves discretized finite statistical games. While these methods work well in the stylized example corresponding to Theorem 1, the authors note that their practical performance in more difficult, higher-dimensional, or otherwise complex decision problems is not yet established and needs investigation.